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Hardy and Carleman type inequalities
2004 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

This thesis deals with various generalizations of the inequalities by Carleman, Hardy and Pólya-Knopp. In Chapter 1 we give an introduction and overview of the area that serves as a frame for the rest of the thesis. In Chapter 2 we consider Carleman's inequality, which may be regarded as a discrete version of Pólya-Knopp's inequality and also as a natural limiting inequality of the discrete Hardy inequality. We present several simple proofs of and \ remarks (e.g. historical) about this inequality. In Chapter 3 we give some sharpenings and generalizations of Carleman's inequality. We discuss and comment on these results and put them into the frame presented in the previous chapter. We also include some new proofs and results. In Chapter 4 we give a new weight characterization of the weighted Hardy inequality for decreasing functions. In Chapter 5 we use the results from Chapter 4 to give a new weight characterization of the weighted Pólya-Knopp inequality for decreasing functions and we also give a new scale of weightconditions for the embedding L^{p}(v) to L^{q}(u) for the case 1

Place, publisher, year, edition, pages
Luleå: Luleå tekniska universitet, 2004. , 75 p.
Series
Licentiate thesis / Luleå University of Technology, ISSN 1402-1757 ; 2004:81
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-26692Local ID: f90d9c20-a55a-11db-8975-000ea68e967bOAI: oai:DiVA.org:ltu-26692DiVA: diva2:999862
Note

Godkänd; 2004; 20070116 (haneit)

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2017-11-24Bibliographically approved

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Johansson, Maria

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